Stuck on an integral

2. The attempt at a solution
The answer is the book made it seem like the rule [itex] \int \frac {du}{u} = ln|u| + C [/itex] was used. Here's what I got:
[tex]u = -t^3 + 9t + 1[/tex]
[tex]du = -3t^2 + 9\;dt[/tex]
[tex]-\frac{1}{3}du = t^2 + 9\;dt[/tex]
Obviously this won't work out, so is there something I'm overlooking that anyone can point out?